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the Coma cluster
P. A. R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, F. Atrio-Barandela, J.
Aumont, C. Baccigalupi, A. Balbi, A. J. Banday, R. B. Barreiro, et al.
To cite this version:
P. A. R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, F. Atrio-Barandela, et al.. Planck intermediate
results X. Physics of the hot gas in the Coma cluster. Astronomy and Astrophysics - A&A, EDP
Sciences, 2013, 554, pp.A140. �10.1051/0004-6361/201220247�. �cea-01135390�
DOI:10.1051/0004-6361/201220247
c ESO 2013
&
Astrophysics
Planck intermediate results
X. Physics of the hot gas in the Coma cluster
Planck Collaboration: P. A. R. Ade
92, N. Aghanim
63, M. Arnaud
78, M. Ashdown
75,6, F. Atrio-Barandela
19, J. Aumont
63, C. Baccigalupi
91, A. Balbi
38, A. J. Banday
101,9, R. B. Barreiro
71, J. G. Bartlett
1,72, E. Battaner
103,
K. Benabed
64,98, A. Benoît
61, J.-P. Bernard
9, M. Bersanelli
35,53, I. Bikmaev
21,3, H. Böhringer
84, A. Bonaldi
73, J. R. Bond
8, J. Borrill
14,95, F. R. Bouchet
64,98, H. Bourdin
38, M. L. Brown
73, S. D. Brown
25, R. Burenin
93, C. Burigana
52,37, P. Cabella
39, J.-F. Cardoso
79,1,64, P. Carvalho
6, A. Catalano
80,77, L. Cayón
32, L.-Y Chiang
67, G. Chon
84, P. R. Christensen
88,40, E. Churazov
83,94, D. L. Clements
59, S. Colafrancesco
49, L. P. L. Colombo
24,72, A. Coulais
77, B. P. Crill
72,89, F. Cuttaia
52, A. Da Silva
12, H. Dahle
69,11, L. Danese
91, R. J. Davis
73, P. de Bernardis
34,
G. de Gasperis
38, A. de Rosa
52, G. de Zotti
48,91, J. Delabrouille
1, J. Démoclès
78, F.-X. Désert
56, C. Dickinson
73, J. M. Diego
71, K. Dolag
102,83, H. Dole
63,62, S. Donzelli
53, O. Doré
72,10, U. Dörl
83, M. Douspis
63, X. Dupac
43,
T. A. Enßlin
83, H. K. Eriksen
69, F. Finelli
52, I. Flores-Cacho
9,101, O. Forni
101,9, M. Frailis
50, E. Franceschi
52, M. Frommert
18, S. Galeotta
50, K. Ganga
1, R. T. Génova-Santos
70, M. Giard
101,9, M. Gilfanov
83,94, J. González-Nuevo
71,91, K. M. Górski
72,105, A. Gregorio
36,50, A. Gruppuso
52, F. K. Hansen
69, D. Harrison
68,75, S. Henrot-Versillé
76, C. Hernández-Monteagudo
13,83, S. R. Hildebrandt
10, E. Hivon
64,98, M. Hobson
6, W. A. Holmes
72,
A. Hornstrup
17, W. Hovest
83, K. M. Hu ff enberger
104, G. Hurier
80, T. R. Ja ff e
101,9, T. Jagemann
43, W. C. Jones
27, M. Juvela
26, E. Keihänen
26, I. Khamitov
97, R. Kneissl
42,7, J. Knoche
83, L. Knox
29, M. Kunz
18,63, H. Kurki-Suonio
26,46,
G. Lagache
63, A. Lähteenmäki
2,46, J.-M. Lamarre
77, A. Lasenby
6,75, C. R. Lawrence
72, M. Le Jeune
1, R. Leonardi
43, P. B. Lilje
69,11, M. Linden-Vørnle
17, M. López-Caniego
71, P. M. Lubin
30, J. F. Macías-Pérez
80, B. Ma ff ei
73, D. Maino
35,53, N. Mandolesi
52,5, M. Maris
50, F. Marleau
66, E. Martínez-González
71, S. Masi
34, M. Massardi
51,
S. Matarrese
33, F. Matthai
83, P. Mazzotta
38,, S. Mei
45,100,10, A. Melchiorri
34,54, J.-B. Melin
16, L. Mendes
43, A. Mennella
35,53, S. Mitra
58,72, M.-A. Miville-Deschênes
63,8, A. Moneti
64, L. Montier
101,9, G. Morgante
52, D. Munshi
92, J. A. Murphy
87, P. Naselsky
88,40, P. Natoli
37,4,52, H. U. Nørgaard-Nielsen
17, F. Noviello
73, D. Novikov
59,
I. Novikov
88, S. Osborne
96, F. Pajot
63, D. Paoletti
52, O. Perdereau
76, F. Perrotta
91, F. Piacentini
34, M. Piat
1, E. Pierpaoli
24, R. Pi ff aretti
78,16, S. Plaszczynski
76, E. Pointecouteau
101,9, G. Polenta
4,49, N. Ponthieu
63,56, L. Popa
65,
T. Poutanen
46,26,2, G. W. Pratt
78, S. Prunet
64,98, J.-L. Puget
63, J. P. Rachen
22,83, R. Rebolo
70,15,41, M. Reinecke
83, M. Remazeilles
63,1, C. Renault
80, S. Ricciardi
52, T. Riller
83, I. Ristorcelli
101,9, G. Rocha
72,10, M. Roman
1, C. Rosset
1,
M. Rossetti
35,53, J. A. Rubiño-Martín
70,41, L. Rudnick
86, B. Rusholme
60, M. Sandri
52, G. Savini
90, B. M. Schaefer
99, D. Scott
23, G. F. Smoot
28,82,1, F. Stivoli
55, R. Sudiwala
92, R. Sunyaev
83,94, D. Sutton
68,75, A.-S. Suur-Uski
26,46, J.-F. Sygnet
64, J. A. Tauber
44, L. Terenzi
52, L. To ff olatti
20,71, M. Tomasi
53, M. Tristram
76, J. Tuovinen
85, M. Türler
57,
G. Umana
47, L. Valenziano
52, B. Van Tent
81, J. Varis
85, P. Vielva
71, F. Villa
52, N. Vittorio
38, L. A. Wade
72, B. D. Wandelt
64,98,31, N. Welikala
63, S. D. M. White
83, D. Yvon
16, A. Zacchei
50, S. Zaroubi
74, and A. Zonca
30(Affiliations can be found after the references) Received 17 August 2012/Accepted 26 November 2012
ABSTRACT
We present an analysis ofPlancksatellite data on the Coma cluster observed via the Sunyaev-Zeldovich effect. Thanks to its great sensitivity, Planckis able, for the first time, to detect SZ emission up tor ≈ 3×R500. We test previously proposed spherically symmetric models for the pressure distribution in clusters against the azimuthally averaged data. In particular, we find that the Arnaud et al. (2010, A&A, 517, A92)
“universal” pressure profile does not fit Coma, and that their pressure profile for merging systems provides a reasonable fit to the data only at r <R500; byr = 2×R500 it underestimates the observedyprofile by a factor of2. This may indicate that at these larger radii either: i) the cluster SZ emission is contaminated by unresolved SZ sources along the line of sight; or ii) the pressure profile of Coma is higher atr > R500
than the mean pressure profile predicted by the simulations used to constrain the models. ThePlanckimage shows significant local steepening of theyprofile in two regions about half a degree to the west and to the south-east of the cluster centre. These features are consistent with the presence of shock fronts at these radii, and indeed the western feature was previously noticed in the ROSAT PSPC mosaic as well as in the radio.
UsingPlanckyprofiles extracted from corresponding sectors we find pressure jumps of 4.9+−00..42and 5.0+−10..31in the west and south-east, respectively.
Assuming Rankine-Hugoniot pressure jump conditions, we deduce that the shock waves should propagate with Mach numberMw=2.03+−00..0904and Mse =2.05+−00..2502in the west and south-east, respectively. Finally, we find that theyand radio-synchrotron signals are quasi-linearly correlated on Mpc scales, with small intrinsic scatter. This implies either that the energy density of cosmic-ray electrons is relatively constant throughout the cluster, or that the magnetic fields fall offmuch more slowly with radius than previously thought.
Key words.galaxies: clusters: individual: Coma cluster – galaxies: clusters: intracluster medium – X-rays: galaxies: clusters – cosmology: observations – galaxies: clusters: general – cosmic background radiation
Corresponding author: P. Mazzotta,mazzotta@roma2.infn.it
Article published by EDP Sciences A140, page 1 of19
1. Introduction
The Coma cluster is the most spectacular Sunyaev-Zeldovich (SZ) source in thePlancksky. It is a low-redshift, massive, and hot cluster, and is sufficiently extended that Planckcan resolve it well spatially. Its intracluster medium (ICM) was observed in SZ for the first time with the 5.5 m OVRO telescope (Herbig et al. 1992, 1995). Later, it was also observed with MSAM1 (Silverberg et al. 1997), MITO (De Petris et al. 2002), VSA (Lancaster et al. 2005) and WMAP (Komatsu et al. 2011) which detected the cluster with signal-to-noise ratio ofS/N = 3.6.
As reported in the all-sky early Sunyaev-Zeldovich cluster pa- per,Planckdetected the Coma cluster with aS/N >22 (Planck Collaboration 2011d).
Coma has also been extensively observed in the X-rays from the ROSAT all-sky survey and pointed observations (Briel et al.
1992; White et al. 1993), as well as via a huge mosaic by XMM-Newton(e.g.Neumann et al. 2001,2003;Schuecker et al.
2004). The X-ray emission reveals many spatial features indi- cating infalling sub-clusters such as NGC 4839 (Dow & White 1995;Vikhlinin et al. 1997;Neumann et al. 2001,2003) , tur- bulence (e.g.Schuecker et al. 2004;Churazov et al. 2012) and further signs of accretion and strong dynamical activity.
Moreover, the Coma cluster hosts a remarkable giant ra- dio halo extending over 1 Mpc, which traces the non-thermal emission from relativistic electrons and magnetic fields (e.g.
Giovannini et al. 1993; Brown & Rudnick 2011). The radio halo’s spectrum and extent require an ongoing, distributed mech- anism for acceleration of the relativistic electrons, since their ra- diative lifetimes against synchrotron and inverse Compton losses are short, even compared to their diffusion time across the cluster (e.g.Sarazin 1999;Brunetti et al. 2001). The radio halo also ap- pears to exhibit a shock front in the west, also seen in the X-ray image, and is connected at larger scales with a huge radio relic in the south-west (Ensslin et al. 1998;Brown & Rudnick 2011).
In this paper we present a detailed radial and sector anal- ysis of the Coma cluster as observed byPlanck. These results are compared with X-ray and radio observations obtained with XMM-Newtonand the Westerbork Synthesis Radio Telescope.
We useH0 = 70 km s−1Mpc−1,Ωm = 0.3 andΩΛ = 0.7, which imply a linear scale of 27.7 kpc arcmin−1 at the distance of the Coma cluster (z=0.023). All the maps are in Equatorial J2000 coordinates.
2. ThePlanck frequency maps
Planck1(Tauber et al. 2010;Planck Collaboration 2011a) is the third-generation space mission to measure the anisotropy of the cosmic microwave background (CMB). It observes the sky in nine frequency bands covering 30–857 GHz with high sensitiv- ity and angular resolution from 31 to 5. The Low Frequency Instrument (LFI;Mandolesi et al. 2010;Bersanelli et al. 2010;
Mennella et al. 2011) covers the 30, 44, and 70 GHz bands with amplifiers cooled to 20 K. The High Frequency Instrument (HFI;Lamarre et al. 2010;Planck HFI Core Team 2011a) covers the 100, 143, 217, 353, 545, and 857 GHz bands with bolome- ters cooled to 0.1 K. Polarisation is measured in all but the highest two bands (Leahy et al. 2010;Rosset et al. 2010). A
1 Planck (http://www.esa.int/planck) is a project of the European Space Agency (ESA) with instruments provided by two sci- entific consortia funded by ESA member states (in particular the lead countries: France and Italy) with contributions from NASA (USA), and telescope reflectors provided in a collaboration between ESA and a sci- entific consortium led and funded by Denmark.
combination of radiative cooling and three mechanical cool- ers produces the temperatures needed for the detectors and op- tics (Planck Collaboration 2011b). Two data processing centres (DPCs) check and calibrate the data and make maps of the sky (Planck HFI Core Team 2011b;Zacchei et al. 2011).Planck’s sensitivity, angular resolution, and frequency coverage make it a powerful instrument for Galactic and extragalactic astrophysics as well as for cosmology. Early astrophysics results are given in Planck Collaboration VIII-XXVI 2011, based on data taken between 13 August 2009 and 7 June 2010.
This paper is based on the Planck nominal survey of 14 months, i.e. taken between 13 August 2009 and 27 November 2010. The whole sky has been covered two times. We refer to Planck HFI Core Team(2011b) andZacchei et al.(2011) for the generic scheme of time ordered information (TOI) processing and map making, as well as for the technical characteristics of the maps used. We adopt a circular Gaussian beam pattern for each frequency as described in these papers. We use the full-sky maps in the ninePlanckfrequency bands provided in HEALPix (Górski et al. 2005)Nside = 2048 resolution. An error map is associated with each frequency band and is obtained from the difference of the first half and second half of thePlanck rings for a given position of the satellite, but are basically free from astrophysical emission. However, they are a good representa- tion of the statistical instrumental noise and systematic errors.
Uncertainties in flux measurements due to beam corrections, map calibrations and uncertainties in bandpasses are expected to be small, as discussed extensively in Planck Collaboration (2011d,c,e).
3. Reconstruction and analysis of they map
The Comptonisation parameterymaps used in this work have been obtained using the MILCA (modified internal linear combi- nation algorithm) method (Hurier et al. 2010) on thePlanckfre- quency maps from 100 GHz to 857 GHz in a region centred on the Coma cluster. MILCA is a component separation approach aimed at extracting a chosen component (in our case the thermal Sunyaev Zeldovich, tSZ, signal) from a multi-channel set of in- put maps. It is based mainly on the well known ILC approach (see for exampleEriksen et al. 2004), which searches for the lin- ear combination of input maps that minimises the variance of the final reconstructed map while imposing spectral constraints.
For this work, we apply MILCA using two constraints, the first to preserve they signal and the second to remove CMB con- tamination in the finalymap. Furthermore, we correct for the bias induced by the instrumental noise, and we simultaneously use the extra degrees of freedom (d.o.f.) to minimise residuals from other components (2 d.o.f.) and from the instrumental noise (2 d.o.f.). These would otherwise increase the variance of the final reconstructedymap. The noise covariance matrix is esti- mated from jack-knife maps. To improve the efficiency of the algorithm we perform our separation independently on several bins in the spatial-frequency plane. The finalymap has an effec- tive point spread function (PSF) with a resolution of 10FWHM.
Finally, to characterise the noise properties, such as correlation and inhomogeneities, we use jack-knife and redundancy maps for each frequency and apply the same linear transformation as used to compute the MILCAymap. The MILCA procedure pro- vides us with a data mapytogether with random realisations of an additive noise model dy, which is Gaussian, correlated, and may present some non-stationary behaviour across the field of view. These maps are used to derive radial profiles and to per- form the image analysis, as described below.
We verified that the reconstruction methods GMCA (Bobin et al. 2008) and NILC (Remazeilles et al. 2011) give results that are consistent within the errors with the MILCA method (see Planck Collaboration 2013).
3.1. Analysis of radial profiles
In this paper, we present various radial profilesy(r) of the 2D dis- tribution of the Comptonisation parametery. These allow us to study the underlying pressure distribution of the ICM of Coma.
Theyparameter is proportional to the gas pressureP = nekT integrated along the line of sight:
y= σT
mec2
P(l)dl, (1)
wherene and T are the gas electron density and temperature, σTis the Thomson cross-section,kthe Boltzmann constant,me
the mass of the electron and cthe speed of light. All the ra- dial profilesy(r) are extracted from theymap after masking out bright radio sources. In this work we model the observedy(r) projected profiles using the forward approach described in detail by e.g.Bourdin & Mazzotta(2008). We assume that the three- dimensional pressure profiles can be adequately represented by some analytic functions that have the freedom to describe a wide range of possible profiles. The 3D model is projected along the line of sight, assuming spherical symmetry and convolved with the Planck PSF to produce a projected model function f(r).
Finally we fit f(r) to the data using a χ2 minimisation of its distance from the radial profilesy(r)+dy(r) derived from the MILCA map (y(r)) and 1000 realization of its additive noise model (dy(r)). Theχ2 is calculated in the principal component basis of these noise realisations. This procedure uses an ortho- gonal transformation to diagonalise the noise covariance matrix which, thus, decorrelates the additive noise fluctuation.
It is important to say that, as the parameters of the fitting functions are highly degenerate, we adopt two techniques to quantify the uncertainties, i) for each individual parameter; and ii) for the overall model (that is, the global model envelope).
More specifically, the confidence intervals on each pa- rameter are calculated using the percentile method; i.e., we rank the fitted values and select the value corresponding to the chosen percentile. Suppose that our 1000 realizations for a specific parameter ζ are already ranked from bottom to top, the percentile confidence interval at 68.4% corresponds to [ζ158th, ζ842th]. Notice that in this work the confidence inter- vals are reported with respect to the best-fit value obtained by fitting the model to the initial data set.
The envelope of the profiles shown in Figs.5–7,11–14de- limit, instead, the first 684 out of the 1000 model profiles with the lowestχ2. Note that, by design, the forward approach tests the capability of a specific functional to globally reproduce the observed data. For this reason, the error estimates represent the uncertainties on the parameters of the fitting function rather than the local uncertainties of the deprojected quantity. This tech- nique has been fully tested on hydrodynamic simulations (e.g.
Nagai et al. 2007;Meneghetti et al. 2010).
3.2. Zero level of theymap and the maximum detection radius
As a result of the extraction algorithm,Planckymaps contain an arbitrary additive constantyoff which is a free parameter in all oury-map models. This constant can be determined using
Fig. 1.Upper panel: radial profile ofyin a set of circular annuli centred on Coma. The blue curve is the best fitting simple model to the profile over the radial range from 85 arcmin to 300 arcmin. The model con- sists of a power law plus a constantyoff. The best fitting value ofyoffis shown with the dashed horizontal line. Two vertical lines indicate the range of radii used for fitting.Lower panel: the probability of finding an observed value ofy > yComain a given annulus. The probability was estimated by measuringyin a set of annuli with random centres in any part of the image outside 5×R500, whereR500=47 arcmin.
the Planck patch by simply setting to zero the y value mea- sured at very large radii, where we expect to have small or no contribution to the signal from the Cluster itself. In particu- lar, in the case of the 13.6 deg×13.6 deg MILCA-based patch of the image centred on Coma, this constant is negative, as il- lustrated in Fig.1. The radial profile ofy was extracted from the y map in a set of circular annuli centred at (RA, Dec) = (12h59m47s,+27◦5553). The errors assigned to the points are crudely estimated by calculating the variance of the y map blocked to a pixel size much larger than the size of thePlanck PSF. The variance is then rescaled for each annulus, assuming that the correlation of the noise can be neglected on these spatial scales. For a model consisting of a power law plus a constant (over the radial range from 85 arcmin to 300 arcmin) we find yoff =−6.3×10−7±0.9×10−7. We note that the precise value ofyoff depends weakly on the particular model used, and on the range of radii involved in the fitting.
To determine the maximum radius at whichPlanckdetects a significant excess of y compared to the rest of the image, we adopted the following procedure. For every annulus around Coma with measuredy = yComa we have calculated the distri- bution ofy =yrandom measured in 300 annuli of a similar size, but with the centres randomly placed in any part of the image outside the 5×R500circle around Coma, whereR500is the radius at which the cluster density contrast isΔ =500. When calculat- ingyrandomthe parts of the annuli within 5×R500were excluded.
The comparison ofyComawith the distribution ofyrandomis used to conservatively estimate the probability of gettingy > yComa
by chance in an annulus of a given size at a random position in the image (see Fig.1, lower panel). For the annulus between 2.6 and 3.1R500(122 arcmin to 147 arcmin) the probability of
gettingyComaby chance is ≈3×10−3 (a crude estimate, given N = 300 random positions). For smaller radii the probability is much lower, while at larger radii the probability of gettingy in excess ofyComais∼10% or higher. We conclude thatPlanck detects the signal from Coma in narrow annuliΔR/R = 0.2 at least up toRmax ∼3×R500. This is a conservative and model- independent estimate. In the rest of the paper we use paramet- ric models which cover the entire range of radii to fully exploit Planckdata even beyondRmax.
4.XMM-Newton data analysis
TheXMM-Newtonresults presented in this paper have been de- rived from analysis of the mosaic obtained by combining 27 XMM-Newton pointings of the Coma cluster available in the archive. TheXMM-Newtondata have been prepared and anal- ysed using the procedure described in detail inBourdin et al.
(2011), andBourdin & Mazzotta(2008). We estimated theYX= Mgas×T parameter of Coma iteratively using theYX −M500 scaling relation calibrated from hydrostatic mass estimates in a nearby cluster sample observed withXMM-Newton(Arnaud et al. 2010); we findR500≈(47±1)arcmin≈(1.31±0.03) Mpc and we use this value throughout the paper. To study the sur- face brightness and temperature radial profiles we use the for- ward approach described inBourdin et al.(2011) taking care to project the temperature profile using the formula appropriate for spectroscopy; i.e., we use the spectroscopic-like temperature in- troduced byMazzotta et al.(2004).
5. The Comay maps
The main goal of this paper is to present the radial and sectoral properties of the SZ signal from the Coma cluster. Here we de- scribe some general properties of the image; the full image anal- ysis will be presented in a forthcoming paper that will make use of all thePlanckdata, including the extended surveys.
Figure 2 shows the Planck y map of the Coma clus- ter obtained by combining the HFI channels from 100 GHz to 857 GHz. The effective PSF of this map corresponds to FWHM=10and its noise level isσnoise=2.3×10−6.
To highlight the spatial structure of theymap, in Fig.2we overlay the contour levels of theysignal. We notice that at this resolution, theysignal observed by Plancktraces the pressure distribution of the ICM up toR500. As is already known from X-ray observations (e.g.Briel et al. 1992; White et al. 1993;
Neumann et al. 2003), thePlanckymap shows that the gas in Coma is elongated towards the west and extends in the south- west direction toward the NGC 4839 subgroup. Fig.2shows that the SZ signal from this subgroup is clearly detected byPlanck (see the white cross to the south-west).
Figure2also shows clear compression of the isocontour lines in a number of cluster regions. We notice that, in most cases, the extent of the compression is of the order of theymap cor- relation length (≈10): it is likely that most of these are image artifacts induced by correlated noise in theymap. Nevertheless, we also notice at least two regions where the compression of the isocontour lines extends over angular scales significantly larger than the noise correlation length. These two regions, located to the west and to the southeast of cluster centre, may indicate real steepenings of the radial gradient. Such steepenings suggest the presence of a discontinuities in the cluster pressure profile, which may be produced by a thermal shocks, as we discuss in Sect.7. For convenience, in Fig.2we outline the regions from
which we extract theyprofiles used in Sect.7with white sec- tors. It is worth noting that the western steepening extends over a much larger angular scale than indicated by the white sector.
In Sect.7we explain why we prefer a narrower sector for our quantitative analysis.
In Fig. 3 we show the Planck y map of the Coma cluster obtained by adding the 70 GHz channel of LFI to the HFI chan- nels and smoothing to a lower resolution. The PSF of this map corresponds toFWHM = 30, which lowers the noise level by approximately one order of magnitude with respect to the 10 resolution map:σnoise30 = 3.35×10−7. As for Fig. 2the out- ermost contour level indicatesy = 2×σnoise30 = 6.7×10−7. Due to the larger smoothing, this map shows less structure in the cluster centre, but clearly highlights thatPlanckcan trace the pressure profile of the ICM well beyondR200≈2×R500(see the outermost circle in Fig.3).
6. Azimuthally averaged profile
Before studying the azimuthally averaged SZ profile of the Coma cluster in detail, we first show a very simple performance test. In Fig.4we compare the SZ effect toward the Coma cluster, in units of the Rayleigh-Jeans equivalent temperature, measured by Planck and by WMAP using the optimal V and W bands (from Fig. 14 ofKomatsu et al. 2011). This figure shows that, in addition to its greatly improved angular resolution, Planck frequency coverage results in errors on the profile which are
≈20 times smaller than those from WMAP. Thanks to this higher sensitivityPlanckallows us to study, for the first time, the SZ signal of the Coma cluster to its very outermost regions. We do this by extracting the radial profile in concentric annuli centred on the cluster centroid (RA, Dec)=(12h59m47s,+27◦5553).
We fit the observedyprofile using the pressure formula pro- posed byArnaud et al.(2010):
P(x)= P0
(c500x)γ[1+(c500x)α](β−γ)/α, (2) where,x =(R/R500). This is done by fixingR500at the best-fit value obtained from the X-ray analysis (R500 = 1.31 Mpc, see Sect. 4) and using three different combinations of parameters which we itemise below:
– a “universal” pressure model (which we will refer to as Model A) for which we leave onlyP0 as a free parameter and fixc500 = 1.177,γ=0.3081,α =1.0510,β= 5.4905 (Arnaud et al. 2010);
– a pressure profile appropriate for clusters with disturbed X-ray morphology (Model B) for which we leaveP0 as a free parameter and fixc500=1.083,γ=0.3798,α=1.406, β=5.4905 (Arnaud et al. 2010);
– a modified pressure profile (Model C) for which we let all the parameters vary (exceptR500).
The best-fit parameters, together with their 68.4% confidence level errors, are reported in Table1. The resulting best-fit mod- els, together with the envelopes corresponding to the 68.4% of models with the lowestχ2, are overlaid in the upper left, upper right and lower left panels of Fig.5, for models A, B, and C, re- spectively. We find that Eq. (2) fits the observedyprofile only if all the parameters (except R500) are left free to vary (i.e., Model C).
We also fit the observed radialyprofile using a fitting for- mula (Model D) derived from the density and temperature func- tionals introduced byVikhlinin et al.(2006):
P=ne×kT, (3)
6.00 195.50 195.00 194.50 194.00
28.50 28.00 27.50 27.00 500 kpc
Fig. 2.ThePlanckymap of the Coma cluster obtained by combining the HFI channels from 100 GHz to 857 GHz. North is up and west is to the right. The map is corrected for the additive constantyoff. The final map bin corresponds toFWHM =10. The image is about 130 arcmin× 130 arcmin. The contour levels are logarithmically spaced by 21/4 (every 4 lines,yincreases by a factor 2). The outermost contour corresponds to y=2×σnoise=4.6×10−6. The green circle indicatesR500. White and black crosses indicate the position of the brightest galaxies in Coma. The white sectors indicate two regions where theymap shows a local steepening of the radial gradient (see Sect.7and Fig.6).
where
n2e(r) = n20 (r/rc)−α [1+(r/rc)2]3β−α/2
1 [1+(r/rs)3] /3 + n202
[1+(r/rc2)2]3β2, (4)
and
T(r)=T0 (r/rt)−a
[1+(r/rt)b]c/b· (5)
Notice that, for our purpose, Eq. (3) is only used to fit the clus- ter pressure profile. For this reason, it is unlikely that, when
considered separately, the best-fit parameters of Eqs. (4) and (5) reproduce the actual cluster density and temperature profiles.
The best-fit parameters, together with their 68.4% confidence level errors, are reported in Table2.
The resulting model, with the 68.4% envelope is overlaid in the lower-right panel of Fig.5. The above temperature and den- sity functions contain many more free parameters than Eq. (2).
All these parameters have been specifically introduced to ade- quately fit all the observed surface brightness and temperature profiles of X-ray clusters of galaxies. This function, thus, is capable, in principle, of providing a better fit to any observed SZ profile. Despite this, we find that compared with Model C,
197.00 196.00 195.00 194.00 193.00
30.0029.0028.0027.0026.00
500 kpc
Fig. 3.ThePlanckymap of the Coma cluster obtained by combining the 70 GHz channel of LFI and the HFI channels from 100 GHz to 857 GHz. The map has been smoothed to have a PSF withFWHM = 30. The image is about 266 arcmin×266 arcmin. The outermost contour corresponds toy=2×σnoise30=6.7×10−7. The green circles indicate R500and 2×R500≈R200.
Model D does not improve the quality of the fit. The reducedχ2 of model D is slightly higher (Δχ2 =0.3) than for model C.
7. Pressure jumps
Figure2shows at least two cluster regions where theyisocon- tour lines appear to be compressed on angular scales larger than the correlation length of the noise map. This indicate a local steepening of theysignal. The most prominent feature is located at about 0.5 degrees from the cluster centre to the west. Its posi- tion angle is quite large and extends from 340 deg to 45 deg. The second, less prominent feature, is located at 0.5 degrees from the cluster center to the south-east.
Both features suggest the presence of discontinuities in the underlying cluster pressure profiles. To test this hypothesis and to try to estimate the amplitude and the position of the pressure jumps we use the following simplified approach: i) we select two sectors; ii) we extract theyprofiles using circular annuli;
and iii) assuming spherical symmetry, we fit them to a 3D pres- sure model with a pressure jump. This test requires that the ex- traction sectors are carefully selected. Ideally one would like to follow, as close as possible, the curvature of theysignal around the possible pressure jumps. It is clear, however, that this proce- dure cannot be done exactly but it may be somewhat arbitrary.
The pressure jumps are unlikely to be perfectly spherically sym- metric, thus, the sector selection depends also on what is ini- tially thought to be the leading edge of the underlying pressure jump. Despite of this arbitrariness, our approach remain valid for the purpose of testing for the presence of a shock. As matter of fact, even if we choose a sector that does not properly sam- ple the pressure jump, our action goes in the direction of mixing
Fig. 4.Comparison of the radial profile of the SZ effect towards the Coma cluster, in units of the Rayleigh-Jeans equivalent temperature measured byPlanck(crosses) with the one obtained by WMAP (open squares) using the optimalVandWband data (from Fig. 14 ofKomatsu et al. 2011). The plottedPlanckerrors are the square root of the diago- nal elements of the covariance matrix. Notice that profiles have been ex- tracted from SZ maps with 10and 30angular resolution fromPlanck and WMAP, respectively.
the signal from the pre- and post-pressure jump regions. This will simply result is a smoother profile which, when fitted with the 3D pressure model, will returns a smaller amplitude for the pressure jump itself. Thus, in the worst scenario, the measured pressure jumps would, in any case, represent a lower estimate of the jumps at the leading edges.
In order to minimise the mixing of pre- and post-shock sig- nals, one can reduce the width of the analysis sector to the limit allowed by signal statistics. Indeed, for very high signal- to-noise, one could, in principle, extract the y signal along a line perpendicular to the leading edge of the shock. This would limit mixing of pre- and post shock signals to line-of-sight and beam effects. In the specific case of the Coma cluster we notice that the west feature is located in a higher signal-to-noise region than the south-east one. For this reason we decide to extract the west profile using a sector with an angular aperture smaller than the actual angular extent of this feature in theymap.
Following the above considerations, we set the centres and orientations of the west and the south-east sectors to the values reported in the first three columns of Table3and indicated in Fig.2. In Sect. 9.3below we demonstrate that, within the se- lected sectors, the SZ and the X-ray analyses give consistent results. This indicates that, despite the apparent arbitrariness in sector selection: i) these SZ-selected sectors are representative of the features under study and; ii) that the hypothesis of spherical symmetry is a good approximation, at least within the selected sectors.
We fit the profiles using a 3D pressure model composed of two power laws with indexη1andη2and a jump by a factorDJ
at radiusrJ. It is important to note that, even if irrelevant for the estimate of the jump amplitude, the value of both the slopeη2
and the absolute normalization of the 3D pressure at a given ra- dius depends on the slope and extension of the ICM along the line of sight. To take this into account we assume that outside the fitting region (i.e. atr>rs, withrs=2 Mpc) the slope of the pressure profile follows the asymptotic average pressure profile corresponding to model C (i.e.η3 = β = 3.1; see Sect.6and
Table 1. Best-fit parameters for theArnaud et al.(2010) pressure model Eqs. (4) and (5).
Model P0 c500 γ α β R500
(Mpc) (10−2cm−3keV) (Mpc)
A (“Universal”) 2.57+−0.040.04 1.17 0.308 1.051 5.4905 1.31 B (“Universal” merger) 1.08+−00..0202 1.083 0.3798 1.406 5.49 1.31 C (“Universal” all free) 2.2+−00..34 2.9+−00..32 <0.001 1.8+−00..52 3.1+−00..52 1.31
Table1). The 3D pressure profile is thus given by:
P=P0×⎧⎪⎪⎪⎨
⎪⎪⎪⎩
DJ(r/rJ)−η1 r<rJ
(r/rJ)−η2 rJ<r<rs
(rs/rJ)−η2(r/rs)−η3, r>rs. (6) We project the above 3D pressure model, integrating along the line of sight forr<10 Mpc.
The best-fit parameters, together with their 68.4% errors, are reported in Table 3. Note, that the error bars on rJ are smaller than the angular resolution ofPlanck. As explained in AppendixA, this is not surprising and is simply due to projec- tion effects.
In the left and right panels of Fig.7 we show with a grey shadow the corresponding 3D pressure jump models with their errors for the west and south-east sectors, respectively. For con- venience in Fig.6 we overlay the data points with the best-fit projectedy models after and before the convolution with the PlanckPSF. As shaded region, we report the envelope derived from the 68.4% of models with the lowestχ2. In the lower pan- els we show the ratio between the data and the best-fit model of the projectedyprofile in units of the relative error. This fig- ure clearly shows that the pressure jump model provides a good fit to the observed profiles for both the west and south-east sec- tors. Furthermore the comparison of the projected model before and after the convolution with the PSF clearly shows that, for the Coma cluster, the effect of thePlanck PSF smoothing is secondary with respect to projection effects. This indicates that there is only a modest gain, from the detection point of view, in observing this specific feature using an instrument with a much better angular resolution thanPlanck (for a full discussion, see AppendixA).
As reported in Table3the pressure jumps corresponding to the observed profiles areDJ =4.9+0.4−0.2andDJ = 5.0+1.3−0.1for the west and south-east sectors, respectively.
8. SZ-radio comparison
In Fig. 8 we overlay the y contour levels from Fig. 2 with the 352 MHz Westerbork Synthesis Radio Telescope diffuse to- tal intensity image of the Coma cluster from Fig. 3 ofBrown
& Rudnick(2011). Most of the emission from compact radio sources both in and behind the cluster has been automatically subtracted. This image clearly shows a correlation between the diffuse radio emission and theysignal.
To provide a more quantitative comparison of the observed correlation, we first removed the remaining compact source emission in the radio image using the multiresolution filtering technique ofRudnick(2002). This removed 99.9% of the flux of unresolved sources, although residual emission likely associ- ated with the tailed radio galaxy NGC 4874 blends in to the halo emission and contributes to the observed brightness within the central∼300 kpc. After filtering, we convolve the the diffuse ra- dio emission to 10 arcmin resolution to match thePlanckymap.
Table 2. Best-fit parameters for pressure model D Eq. (3) (Vikhlinin et al. 2006).
Density Temperature
n0 (10−3cm−3) 2.9+0.1−0.3 T0 (KeV) 6.9+0.1−0.8 rc (Mpc) 0.4+−0.020.2 rt (Mpc) 0.26+−0.070.05 rs (Mpc) 0.7+−00..22 a 0
α <10−6 b 3.4+−50..02
β 0.57+−00..023 c 0.6+−00..71
γ 3
1.3+−0.70.7 n02 (cm−3) 0a
Notes.As this model is used to fit the pressure, the best-fit density and temperature profiles are highly correlated and are unlikely to describe the actual cluster density and temperature profiles (see text).(a)The fit returnsn02=0 thusrc2andβ2are arbitrary.
We then extract the radio andysignals from ther<50 arcmin region of the cluster and plot the results in Fig.9. This is the first quantitative surface-brightness comparison of radio and SZ brightnesses2. We fit the data in the log–log plane using the Bayesian linear regression algorithm proposed byKelly(2007), which accounts for errors in both abscissa and ordinate. The radio errors of 50 mJy/10 beam are estimated from the off- source scatter, which is dominated by emission over several de- gree scales which is incompletely sampled by the interferometer.
We find a quasi-linear relation between the radio emission and theysignal:
y
10−5 =10(0.86±0.02)FR(0.92±0.04), (7) whereFRis the radio brightness in Jy beam−1(10 arcmin beam FWHM).
Furthermore, using the same algorithm, we find that the in- trinsic scatter between the two observables is only (9.6±0.2)%.
The quasi-linear relation between the radio emission andysig- nal, and its small scatter, are also clear from the good match of the radio andyprofiles shown in Fig. 10, obtained by simply rescaling the 10FWHM convolved radio profile by 100.86×105. An approximate linear relationship between the radio halo and SZ total powers for a sample of clusters was also found byBasu (2012), for the case that the signals are calculated over the vol- ume of the radio halos.
There are several sources of scatter contributing to the point- by-point correlation in Fig. 9 and the radial radio profile in Fig.10. First is the random noise in the measurements, which is∼2–3 mJy/135beam. Even after convolving to a 10beam, however, this is insignificant with respect to the other sources
2 See e.g.Ferrari et al.(2011) andMalu & Subrahmanyan(2012) for a morphological comparison between radio and SZ brightnesses.
Fig. 5.Comparison between the azimuthally averagedyprofile of the Coma cluster and various models. Fromleft to right, top to bottom, we show the best-fitymodels corresponding to the Arnaud et al. (2010) “universal” profile (A), the “universal” profile for merger systems (B), the modified “universal” profile (C, see1), and the Vikhlinin et al. fitting formula (D, see.2). For each panel we show in theUpper subpanelthe points indicating the Comayprofile extracted in circular annuli centred at (RA, Dec)=(12h59m47s,+27◦5553). The plotted errors are the square root of the diagonal elements of the covariance matrix. Continuous and dotted lines are the best-fit projectedymodel after and before the convolution with thePlanckPSF, respectively. The gray shaded region indicates the envelope derived from the 68.4% of models with the lowestχ2. In the lower subpanelwe show the ratio between the observed and the best-fit model of the projectedyprofile in units of the relative error. The gray shaded region indicates the envelope derived from the 68.4% of models with the lowestχ2.
of scatter. A second issue is the proper zero-level of the ra- dio map, based on the incomplete sampling of the largest scale structures by the interferometer. After making our best esti- mate of the zero-level correction, the remaining uncertainty is
∼25 mJy/10beam, which is indicated as error bars in Fig.10.
Note that the radio profile is significantly flatter at large radii than presented by Deiss et al. (1997). However, their image, made with the Effelsberg 100 m telescope at 1.4 GHz, appears to have set the zero level too high; they do not detect the faint Coma related emission mapped byBrown & Rudnick(2011) on the Green Bank Telescope, also at 1.4 GHz, and by Kronberg et al.(2007) at 0.4 GHz using Arecibo and DRAO. The addition of a zero level flux to theDeiss et al.(1997) measurements at their lowest contour level flattens out their profile to be consis- tent with ours at their furthest radial sample at 900 kpc.
Finally, there are azimuthal variations in the shape of the ra- dial profile, both for the radio andY images. This is seen most clearly in Fig.6, comparing the west and southeast sectors. In the radio, the radial profiles in 90 degree wide sectors differ by up to a factor of 1.6 from the average; it is therefore important to understand Fig.10as an average profile, not one that applies uni- versally at all azimuths. These azimuthal variations can also con- tribute to the scatter in the point-by-point correlation in Fig.9, but only to the extent that the behavior differs between radio andY.
9. Discussion
So far In this paper we have presented the data analysis of the Coma cluster observed in its SZ effect by thePlanck satellite.
Table 3. Best-fit parameters of the pressure jump model of Eq. (6).
Sector aRA aDec aPosition angle P0 rJ DJ η1 η2
(J2000) (J2000) (deg:deg) (10−4cm−3keV) (Mpc)
West 13 00 25.6 +27 54 44.00 340:364 8.8+−00..25 1.13−0.01+0.03 4.9+−0.20.4 0.0+−0.00.2 1.2+−0.20.2 South-east 12 59 48.9 +28 00 14.39 195:240 3.6+−0.50.1 0.92−0.01+0.02 5.0+−0.11.3 1.5+−0.20.2 1.00+−0.50.3
Notes.(a)The RA and Dec indicate the centre of curvature of the sectors from which the profiles have been extracted.(b)We fixedrs=2 Mpc and η3=3.1 (see text).
Fig. 6.Comparison between the projectedyradial profile and the best-fit shock model of the west (left) and south-east (right) pressure jumps.
Upper panels: the points indicate the Comayprofile extracted from the respective sectors, whose centres and position angles are reported in Table3. The plotted errors are the square root of the diagonal elements of the covariance matrix. Continuous and dotted lines are the best-fit projectedymodel reported in Table3after and before the convolution with thePlanckPSF, respectively. The two vertical lines mark the±1σ position range of the jump. The gray shaded region indicates the envelope derived from the 68.4% of models with the lowestχ2.Lower panels:
ratio between the observed and the best-fit model of the projectedyprofile in units of the relative error. The gray shaded region indicates the envelope derived from the 68.4% of models with the lowestχ2.
Fig. 7.68.4% confidence level range of the 3D-pressure model for the west (left panel) and south-east (right panel) sectors in Fig.6. Grey shaded regions are the profiles derived from thePlanckdata. Red regions are the profiles derived from theXMM-Newtondata.
In Sects.5 and6 we showed that, thanks to its great sensitiv- ity,Planckis capable of detecting significant SZ emission above the zero level of they map up to at least 4 Mpc which cor- responds to R ≈ 3×R500. This allows, for the first time, the study of the ICM pressure distribution in the outermost clus- ter regions. Furthermore, we performed a comparison with ra- dio synchrotron emission. Here we discuss our results in more detail.
9.1. Global pressure profile
To study the 3D pressure distribution of the ICM up tor=3−4× R500, we fit the observedy profile using four analytic models summarised in Tables1and2(see Sect.6).
From the ratio plot shown in Fig.5we immediately see that the “universal” pressure profile (Model A) is too steep both in the cluster centre and in the outskirts. The fit to the data thus results
500 kpc 500 kpc 500 kpc
Fig. 8.Westerbork Synthesis Radio Telescope 352 MHz total inten- sity image of the Coma cluster from Fig. 3 of Brown & Rudnick (2011) overlaid with theycontour levels from Fig.2. Most of the ra- dio flux from compact sources has been subtracted; the resolution is 133 arcsec × 68 arcsec at −1.5 degrees (W of N). The white circle indicatesR500.
Fig. 9.Scatter plot between the radio map after smoothing toFWHM= 10and theysignal for the Coma cluster. To make the plot clearer, we show errors only for some points.
in an overestimation and underestimation of the observed SZ sig- nal at smaller and larger radii, respectively. The overestimation of the observed profile at lower radii is consistent with WMAP (Komatsu et al. 2011). This is expected, since merging systems, such as Coma, have a flatter central pressure profile than the
“universal” model (Arnaud et al. 2010). For merging systems, Model B should provide a better fit, as it has been specifically calibrated, atr<R500, to reproduce the average X-ray profiles of such systems (Arnaud et al. 2010). Figure5shows that this latter model indeed reproduces the data well atr<R500. Nevertheless,
Fig. 10.Comparison of they(black) and diffuse radio (red) global ra- dio profiles in Coma. The radio profile has been convolved to 10 arcmin resolution to match thePlanckFWHM and simply rescaled by the mul- tiplication factor derived from the linear regression shown in Fig.9.
The radio errors are dominated by uncertainties in the zero level due to a weak bowling effect resulting from the lack of short interferometer spacings.
Fig. 11.Comparison of the pressure slopes of the best-fit models shown in Fig.5. The red, green, blue and grey lines correspond to Models A, B, C, and D, respectively.
as for Model A, it still underestimates the observedysignal at larger radii. The observed profile clearly requires a shallower pressure profile in the cluster outskirts, as evident in Models C and D. This is important, as the external pressure slopes of both Model A and B are tuned to reproduce the mean slope predicted by the hydrodynamic simulations ofBorgani et al.(2004),Nagai et al.(2007), and Piffaretti & Valdarnini(2008, from now on, B04+N07+P08). ThePlanck observation shows that the pres- sure slope for Coma is flatter than this value. This is also illus- trated in Fig.11where we report the pressure slope as a function of the radius in our models: we find that while atR =3×R500
the mean predicted pressure slope is>4.5 for Models A and B, the observed pressure slope of Coma is≈3.1 as seen in Model C and Model D.
In Fig.12we compare the scaled pressure profile of Coma with the pressure profiles derived from the numerical simula- tions of B04+N07+P08 and with the numerical simulations of
Fig. 12.Scaled Coma pressure profile with relative errors (black line and gray shaded region) overplotted on the scaled pressure profiles de- rived from numerical simulations of B04+N07+P08 (blue line and vi- olet shaded region),Battaglia et al.(2012, red line and shaded region), and Dolag et al. (in prep., green line and light green shaded region).
Dolag et al. (in prep.) andBattaglia et al.(2012). We note that the simulations agree within their respective dispersions across the whole radial range. The Dolag et al. (in prep.) andBattaglia et al.
(2012) profiles best agree within the central part, and are flatter than the B04+N07+P08 profile. This is likely due to the imple- mentation of AGN feedback, which triggers energy injection at cluster centre, balancing radiative cooling and thus stopping the gas cooling. In the outer parts where cooling is negligible, the B04+N07+P08 and Dolag et al. (in prep.) profiles are in perfect agreement. TheBattaglia et al.(2012) profile is slightly higher, but still compatible within its dispersion with the two other sets.
Here again, differences are probably due to the specific imple- mentation of the simulations.
We find that the Coma pressure profile at 2×R500 is al- ready 2 times higher than the average profile predicted by the B04+N07+P08 and Dolag et al. (in prep.) simulations, although still within the overall profile distribution which has quite a large scatter. The pressure profile ofBattaglia et al.(2012) appears to be more consistent with the Coma profile and, in general, with thePlanckSZ pressure profile obtained by stacking 62 nearby massive clusters (Planck Collaboration 2013). Still Fig.12indi- cates that the Coma pressure profile lies on the upper envelope of the pressure profile distribution derived from all the above simulations.
It is beyond the scope of this paper to discuss in detail the comparison between theoretical predictions. Here we just stress that, at such large radii, there is the possibility that the observed SZ signal could be significantly contaminated by SZ sources along the line of sight. This signal could be generated by: i) un- resolved and undetected clusters; and ii) hot-warm gas filaments.
Contamination would produce an apparent flattening of the pres- sure profile. We tested for possible contamination by unresolved clusters by re-extracting theyprofile, excluding circular regions ofr = 5 centred on all NED identified clusters of galaxies
Fig. 13.Comparison between the Planck and XMM-Newton derived deprojected total pressure profiles. Upper panel: blue line and light blue shaded region are the deprojected pressure profile, with its 68.4% confidence level errors, obtained from the X-ray analysis of the XMM-Newtondata (see text). The black line and grey shaded regions are the best-fit and 68.4% confidence level errors from the Model C pressure profile resulting from the fit shown in Fig.5. Lower panel:
ratio between theXMM-NewtonandPlanckderived pressure profiles.
The black line and the grey shading indicate the best-fit and the 68.4%
confidence level errors, respectively.
present in the Coma cluster region. We find that the newypro- file is consistent within the errors with the previous one, which implies that this kind of contamination is negligible in the Coma region. Thus, if there is SZ contamination it is probably related to the filamentary structures surrounding the cluster. We note that from the re-analysis of the ROSAT all-sky survey,Bonamente et al.(2009) andBonamente et al.(2003) report the detection of extended soft X-ray emission in the Coma cluster region up to 5 Mpc from the cluster centre. They propose that this emission is related to filaments that converge toward Coma and is generated either by non-thermal radiation caused by accretion shocks or by thermal emission from the filaments themselves.
9.2. X-ray and SZ pressure profile comparison
We can compare the 3D pressure profile derived from the SZ ob- servations to that obtained by multiplying the 3D electron den- sity and the gas temperature profiles derived from the data anal- ysis of theXMM-Newtonmosaic of Coma.
In Fig.13we compare the 3D X-ray pressure profile with the 3D SZ profile of our reference Model C. We point the reader’s attention to the very large dynamical range shown in the figure:
the radius extends up tor=4 Mpc, probing approximately four orders of magnitude in pressure. In contrast, due to a combi- nation of relatively high background level and available mosaic observations,XMM-Newtoncan probe the ICM pressure profile of Coma only up to∼1 Mpc. This is a four times smaller radius thanPlanck, probing only∼one order of magnitude in pressure.
Due to the good statistics of bothPlanckandXMM-Newton data, we see that the pressure profile derived fromPlanck ap- pears significantly lower than that of XMM-Newton, even if they differ by only 10–15%. This discrepancy may be related
